EXPERIMENTAL STUDY OF THE TIME DOMAIN …arizona.openrepository.com/arizona/bitstream/10150/280457/1/azu_td... · OF THE TIME DOMAIN DAMAGE IDENTIFICATION by ... autocollimator ...
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Experimental study of the timedomain damage identification
Item Type text; Dissertation-Reproduction (electronic)
DEPARTMENT OF CIVIL ENGINEERING & ENGINEERING MECHANICS
In Partially Fulfillment of the Requirements For the Degree of
DOCTOR OF PHILISOPHY WITH A MAJOR IN ENGINEERING MECHANICS
In the Graduate College THE UNIVERSITY OF ARIZONA
2 0 0 3
UMI Number: 3108965
INFORMATION TO USERS
The quality of this reproduction is dependent upon the quality of the copy
submitted. Broken or indistinct print, colored or poor quality illustrations and
photographs, print bleed-through, substandard margins, and improper
alignment can adversely affect reproduction.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if unauthorized
copyright material had to be removed, a note will indicate the deletion.
UMI UMI Microform 3108965
Copyright 2004 by ProQuest Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
ProQuest Information and Learning Company 300 North Zeeb Road
P.O. Box 1346 Ann Arbor, Ml 48106-1346
2
THE UNIVERSITY OF ARIZONA ® GRADUATE COLLEGE
As members of the Final Examination Committee, we certify that we have read the
dissertation prepared by Peter Hoa Vo
entitled EXPERIMENTAL STUDY OF THE TIME DOMAIN DAMAGE
IDENTIFICATION
and recommend that it be accepted as fulfilling the dissertation requirement for the
Degree of Doctor of Philosophy
k V\-j4 (;\-v AcMwya Haldol) 1 ~
1 H. Wirscning ^ Paul— ^
) 2 - / \ l / 0 Date 1
Dati / '
Robert B. FleiscJiman (
Date
Alain I.iOpriely
Date
\ zh \ i ' s Date
Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copy of the dissertation to the Graduate College.
I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement.
VWsl ' \ '2-/ \ \ / 0 3 Achintya Haldat-' Date
3
STATEMENT BY AUTHOR
This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.
Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.
SIGNED:
4
ACKNOWLEDGEMENTS
I would like to express my deepest appreciation to Dr. Achintya Haldar for his
guidance, encouragement, and devotion during my research. The challenge of dealing
with problems and obstacles arising from the experiments at time was unbearable.
Without the continuous support and technical leadership from Dr. Haldar, this
dissertation would never thought to be complete. I am forever indebted to him for that.
I also would like to express my gratitude to Dr. Fleischman, Dr. Wirsching, Dr.
Goriely and Dr. Nikravesh for their time reviewing/contributing to enrich the dissertation.
5
To my parents for their sacrifice and a heartbreaking decision that enabled me to escape
out of my country for freedom to pursue education and to lead an American dream.
6
TABLE OF CONTENTS
LIST OF FIGURES 8
LIST OF TABLES 10
ABSTRACT 11
1. CHAPTER 1-INTRODUCTION 13 1.1. Statement of the Problem 13 1.2. Objective of the Dissertation 16 1.3. Scope of the Dissertation 17 1.4. Literature Review 18 1.5. ILS-UI Algorithm Background 26 1.6. Summary 27
2. CHAPTER 2 - IMPLEMENTATION OF THE ILS-UI ALGORITHM 28 2.1. Introduction 28 2.2. Iterative Least Squares with Unknown Input (ILS-UI) Algorithm 28 2.3. Use of ILS-UI Algorithm with a Fixed-Fixed Beam 32
2.3.1. Mass, Stiffness and Damping Matrices 32 2.3.2. ILS-UI Model for Three-Element Fixed-Fixed Beam 35
2.4. Optimal Number of Node Points for the Fixed Beam 44 2.5. System Identification of the Fixed Beam 49 2.6. System Identification of the Simply Supported Beam 60 2.7. Summary 64
5.2.1. Static Deflection Test 108 5.2.2. Logarithmic Decrement Method 112
5.3. ILS-UI Dynamic Tests 119 5.3.1. Fixed Beam Experiment to Validate the ILS-UI Algorithm 119
5.3.1.1 Optimization of the Beam's Response Amplitude 122 5.3.1.2. Scaled Angular Response 123 5.3.1.3. Post-processing of the Accelerometer Data 130 5.3.1.4. Predicted Elemental Stiffness 132
5.4. Summary 134
6. CHAPTER 6 - VALIDATION OF THE ILS-UI ALGORITHM 135 6.1. Introduction 135 6.2. Root Cause Investigation 135 6.3. Alternative Approach 146
6.4. Experimental Results for the Fixed-Fixed Beam 151 6.4.1. Undamaged Fixed Beam 151 6.4.2. Damaged Fixed Beam 153 6.4.3. Evaluation of the Fixed Beam Test Results 158
6.5. Simply Supported Beam Experiment 159 6.5.1. Test Setup 159 6.5.2. Test Results for the Simply Supported Beam 161 6.5.3. Evaluation of the Simply Supported Test Results 167
Figure 1.1, Concept of system identification 19 Figure 1.2, Classification of system identification and proposed study 22 Figure 2.1, Three-element fixed beam 37 Figure 2.2, Representation of the three- and six-element models. Solid circles
are common node points for the models 45 Figure 2.3, Comparison nodal responses of the fixed beam modeled with 3, 6,
12, and 30 elements 47 Figure 2.4, Comparison nodal responses of the simply supported beam
modeled with 3, 6, 12, and 30 elements 48 Figure 2.5, S ix-element fixed beam 50 Figure 2.6, Typical transverse and angular responses at node 3 for the
undamaged fixed beam 52 Figure 2.7, Defect sizes and locations used in both fixed and simply supported
beam 54 Figure 2.8, Typical transverse and angular responses (shown in red) at node 3
for the damaged fixed beam. Response for the undamaged beam shown in blue 56
Figure 2.9, Typical transverse and angular responses (shown in red) at node 2 for the damaged fixed beam, response for the undamaged beam shown in blue for comparison purposes 59
Figure 2.10, Six-element simply supported beam 61 Figure 3.1, Configuration of test instrument 68 Figure 4.1, Illustration of the numerical integration using trapezoidal rule 83 Figure 4.2, Simple sinusoid, f { t ) - sin(;rf) 87
Figure 4.3, Under-critically damped sinusoid,
f { t ) = [cosicodO + sin(cyrfO]e"^®' 91 Figure 4.4, Ideal and Butterworth low pass filters 95 Figure 4.5, Unfiltered time signal 98 Figure 4.7, Filtered time signal with slope and offset 100 Figure 4.8, Final filtered time signal 100 Figure 4.9, Comparison of filtered signal versus ideal 10 Hz response 102 Figure 4.10, (Left Column) Ideal closed form integration of the 10 Hz response;
(Middle Column) Numerical integration of the 10 Hz filtered signal without removing slope and offset; (Right Column) Numerical integration of the filtered signal with slope and offset removed 106
Figure 5.1, Static deflection test setup 109 Figure 5.2, Logarithmic decrement damping test setup 113 Figure 5.3, Free-decay measurement at midspan of the 76.2 cm fixed beam 116 Figure 5.4, Free-decay measurement at midspan of the 76.2 cm simply
supported beam 117
9
LIST OF FIGURES - Continued
Figure 5.5, Test setup for the fixed beam experiment 120 Figure 5.6, Transverse and angular responses at node 3 124 Figure 5.7, Comparison of the scaled and actual angular response measured at
Node 3 for the fixed beam 129 Figure 5.8, Raw transverse acceleration measured at Node 3 for the
undamaged fixed beam 131 Figure 5.9, Filtered transverse acceleration measured at Node 3 for the
undamaged fixed beam 131 Figure 6.1, Actual noise measurements for accelerometer (top plot) and
autocollimator (bottom plot) 137 Figure 6.2, System identification of a fixed beam using alternative approach 152 Figure 6.3, Damaged fixed beam 155 Figure 6.4, Predicted element stiffnesses using alternative approach for the
fixed beam 156 Figure 6.5, Test setup for the undamaged simply supported beam experiment 160 Figure 6.6, Designation of nodes and elements for the simply supported beam 162 Figure 6.7, Measured responses of the undamaged simply supported beam 164
10
LIST OF TABLES
Table 1.1, Comparison of the proposed method with other SI techniques with unknown input 25
Table 2.1, Predicted element modulus of rigidity of the fixed beam using computer generated nodal responses 57
Table 2.2, Predicted modulus of rigidity for the elements using computer generated nodal responses 63
I Table 4.1, Summary results of numerical integration of f ( t ) - js in f 7a)dt 89
0
1 Table 4.2, Summary results of numerical integration errors, f ( t )= ̂ s in(M)dt 89
0
Table 4.3, Summary results of numerical integration of }
f ( t ) = ^[cos{ cod t ) + s in( cod t ) \e~ '^ '^ 'd t 93 0
Table 4.4, Summary results of numerical integration errors of 1
f( t) = j[cos( codt) + sin( codt 93 0
Table 4.5, Absolute amplitude and phase error due to numerical integration 104 Table 5.1, Fixed beam static deflection test results Ill Table 5.2, Simply supported beam static deflection test results 111 Table 5.3, Measured average stiffness Ill Table 5.4, Rayleigh damping constants {a andP) 118 Table 5.5, Angular-to-transverse scaling ratios for the undamaged fixed beam 127 Table 5.6, Predicted element's stiffness for the fixed beam 133 Table 6.1, Predicted EI for the fixed beam using noise-free and noise-polluted
responses 138 Table 6.2, ILS-UI algorithm convergence with nodal response amplitude error 141 Table 6.3, ILS-UI algorithm convergence with phase shift error 145 Table 6.4, Measured scaling ratios for the fixed beam 149 Table 6.5, ILS-UI algorithm convergence 149 Table 6.6, Quantifiable changes in element stiffnesses using the alternative
approach for the fixed beam 157 Table 6.7, Measured scaling ratios for the undamaged simply supported beam 163 Table 6.8, Measured scaling ratios for the damaged simply supported beam 163 Table 6.9, Quantifiable changes in element stiffnesses using the alternative
approach for the simply supported beam 166
11
ABSTRACT
A theoretical and experimental study was undertaken to validate the use of a novel
time-domain system identification (SI) method for detecting changes in stiffnesses of
uniform cross section fixed-fixed and simply supported beams. By quantifying the
reduction of beam's elemental stiffnesses, the location of damage can be detected. The
Iterative Least Squares (ILS-UI) algorithm, a novel, time-domain SI algorithm, being
developed at the University of Arizona for nondestructive evaluation of structures, is
used for this purpose.
The ILS-UI algorithm requires the use of nodal response time histories to develop an
equivalent multi-degree-of-freedom model in which the number of node points is equal to
the number of sensors used in the experiment. To optimize the number of sensors, a
finite element model was developed in which the beam was discretized into an optimum
number of node points, such that nodal responses at these node points are equivalent to
that of the continuous beam.
As a prelude to the experimental validation, a simulation was performed to study
errors in the numerical integration of a digitized signal for three different rules:
trapezoidal, Simpson's and Boole's. It was shown that Simpson's rule and Boole's rule
yield smaller errors than the trapezoidal rule, especially when lower sampling rates are
used. Several post processing techniques to remove noise, to filter out high frequencies
and remove slope and offset from a data set were also demonstrated.
In the first phase of the validation experiments, the optimum number of node points
was determined for the fixed beam. Also, a method was developed to scale angular
12
response based on the measured transverse response. The ILS-UI algorithm was then
used to predict element stiffnesses for the fixed beam. The stiffness predictions did not
converge. This prompted an investigation to determine the root cause of the failure.
It was found that amplitude and phase errors in the accelerometer's measurements
were the root cause of the failure. After this was determined, an alternative approach was
developed to mitigate the amplitude and phase shift errors.
To validate the alternative approach, nodal responses were measured for the beam
with and without damage. The ILS-UI algorithm was demonstrated to successfully
quantify reduction in the beam's element stiffnesses and the location of damage was
identified.
13
1. CHAPTER 1-INTRODUCTION
1.1. Statement of the Problem
Nondestructive mechanical evaluation of existing, in-service structures is a subject
of great interest and importance to the engineering profession and society at large. An
aging national infrastructure drives the need for tools and techniques with which
engineers can analyze structures and predict failure, but taking a structure out of service
(e.g., shutting down a bridge) for inspection or testing can have a significant economic
impact. What is needed is a tool or method that allows the engineer to evaluate a
structure without taking it out of service, destroying it, or disassembling it. In addition,
the development of a method for localizing damage, i.e., identifying a single damaged
beam, truss, or column among many, would be a great technical advance and benefit to
society.
At present, there is no agreed-upon method for evaluating large, in-service
structures. Often, defects are obvious to the naked eye, and replacement or retrofitting of
the structure is relatively simple. More commonly, defects are not visible, and this raises
questions. How many components should be inspected to assure that the entire structure
is fit for service? How often should it be reinspected? When does the engineer know
that all defects have been found? At what rate are different components degrading? A
method is needed for monitoring and quantifying damage to individual components of a
larger structure when visible defects are not present.
In addition to the routine inspection of in-service structures, there is the issue of
'emergency' inspections of a structure after it has been subjected to an unforeseen or
14
severe load (like an earthquake). Is it safe to open damaged buildings and bridges to the
public after a quake? If it is not, how can the damaged structure be brought up to current
standards? Which components of a structure need to be replaced and which can be kept
under observation? Who decides whether the structure is safe or unsafe and whether it
should be repaired or demolished? These issues came to the attention of the nation after
the 1994 Northridge, California earthquake. One expert commented "There's a lack of
capable, well-trained engineers who understand failure modes. Buildings are being
condemned uimecessarily because the engineers are erring on the conservative side and
reacting to people's fears." (Time Magazine) The expert saw "one office building torn
down before business owners could retrieve company files." He also added "Officials
also condemned a hospital and relocated the occupants to a nearby commercial building
that might have been in a similar condition."
Clearly, there is a lack of practical ideas for detecting and quantifying defects in
existing structures. New, innovative solutions must be sought.
In engineering practice to this point, global problems have been addressed at the
global level and local problems at the local level. For instance, the use of structural
modal analysis provides global information on the structure based on a global response.
If the modal response changes from one inspection to the next, it can be inferred that
something in the structure has changed, but the number, location and magnitude of the
changes are unknown.
Similarly, a local response can be used to perform a local analysis, but this presents
its own set of problems. Assuming that the location and type of defect are knovm, it may
be inaccessible; the available sensors may not be suitable to detect the particular defect;
and it may not be possible to use the method to routinely inspect structures without
disrupting operations, which may cost an excessive amount of money.
The concept proposed here is motivated by the realization that defects begin at the
local level and, depending on their location, magnitude, and rate of change, affect a
structure globally. This third concept, and the subject of this dissertation, is the
prediction of local behavior using global information. (Note that a potential fourth
concept, the prediction of global behavior based on local information is, in most cases, a
non-unique mathematical problem.)
The research presented here is based on the assumption that a large structure is
composed of single, local elements. This is true in a mathematical representation of the
structure (a finite element model, for instance) or in a physical experiment. When
damage occurs in a single element, the element properties (stiffness and damping) will
change. These changes will be reflected in the global response of the structure.
Recent advances in data acquisition, signal processing, and data analysis have made
the System Identification (SI) technique an increasingly useful technique for extracting
element characteristics from global responses. The SI technique serves as the starting
point for the research described here, and will be described in more detail later.
Note that several subjects are excluded from this research. First, the detection of
minute defects that do not cause observable changes in structural behavior is not
considered. All materials have defects; this study is about major defects that alter the
static and dynamic behavior of the structure, causing safety concerns. It should be noted
16
that a minute defect may become a major defect over time, and the method developed in
this dissertation has the potential to detect minute defects as they advance into more
dangerous ones.
Second, the detection of defects so severe that they will cause the structure to
develop nonlinear behavior is beyond the scope of this study. Nonlinear behavior is a
common natural occurrence, but (as will be seen) there are significant hurdles to be
cleared before a method based on linear behavior can be implemented. Extending the
method to consider nonlinear behavior will be a worthwhile exercise only after the
successful implementation of the linear algorithm.
1.2. Objective of the Dissertation
The primary objective of this study is to develop a simple, economical, yet
sophisticated nondestructive evaluation procedure to detect defects in existing and
retrofitted structures (buildings, bridges and similar structures that can be represented by
a finite element algorithm) without disrupting their normal use. To meet this primary
objective, the proposed study aims to do the following:
(1) Develop an SI algorithm that can be used routinely in identifying the location of
defects at the local element level without using any input excitation information;
(2) Conclusively verify the proposed method using the experimental results;
(3) Develop a general procedure for post data processing to mitigate amplitude and
phase errors in the measured nodal response.
17
1.3. Scope of the Dissertation
To meet this primary objective comprehensively, the proposed study is subdivided
into three parts:
(1) Extend a finite element algorithm based on the iterative least-squares
principle being developed at the University of Arizona, denoted hereafter as
the Iterative Least Squares with Unknown Input (ILS-UI). This algorithm is
used to identify stiffness and damping parameters of the structure at the
element level.
(2) Conclusively verify the ILS-UI algorithm with actual nodal responses
measured for a uniform cross section fixed beam and a simply supported
beam. To meet this objective the ILS-UI must be able to:
(a) identifying stiffness of the beam at the element level
(b) accurately identifying a damage and its location in terms of stiffness
reduction
(3) Develop a detailed procedure for post processing of the measured nodal
response data. For instance, assessing a suitable numerical integration
method that produces smallest errors in integrating acceleration to obtain
velocity and displacement; applying curve fittings to remove biases that
resulted from the post-processing of the data and electronic drift in the
accelerometer; and applying filters to remove unwanted frequencies which
perceived as noises in the data, etc.
18
1.4. Literature Review
The System Identification concept has been around for some time and its
applications, strengths and weaknesses are well-documented. Many papers on the
technique can be found in the literature. Until recently, the shortcomings of using SI as a
structural evaluation technique were thought to prohibit its use as an NDE method.
However, in recent years some in the profession have reexamined the technique in light
of developments in sensor technology and data processing (see, e.g., the Structural
Engineers World Congress of 1998.)
The basic SI approach is very simple. There are three components: the input, the
system itself, and the output. For structural applications the input is a loading or
excitation, the system is a mathematical model of the structure (i.e., a finite element
model with global mass, stiffness, and damping matrices), and the output is the response
of the structure (modes, accelerations, displacements, etc.) If the input and output are
known, the system parameters (the model's M, K, and C matrices) can be identified
(Agbabian, 1991).
19
input system system output
Figure 1.1, Concept of system identification
20
There are two major classifications of SI: analyses done in the time domain and
those done in the frequency domain. As is often the case in structural dynamics, the
frequency domain is preferred, as use of time histories requires large amounts of data and
computation time. Most SI analyses today are conducted in the frequency domain, where
modal information is broken down into mode shapes, resonant frequencies, and modal
damping ratios, all of which can be easily compared from one measurement to another.
Unfortimately, frequency domain SI analyses have significant shortcomings. The
primary limitation of frequency domain analyses is that the global dynamic properties
measured in an SI analyses often do not reflect changes to local elements. For instance, a
large fraction of local structural members may be broken without affecting the global
modal response (fundamental frequencies) by more than 2%. Frequency changes of 2%
are observed in structures with no damage or local changes at all, as the result of noise
(Ibanez, 1988). For highly redundant structural systems, even global, structural level
damage may not be detected by modal analysis. Clearly, time-domain techniques are
necessary.
There are two varieties of time-domain SI techniques; those where the input
excitation history is required, and those where it is not (Figure 1.2). It should be obvious
that, no matter the problem, a solution that requires less information to solve is preferable
to one that requires more. Beyond this fundamental preference for simplicity, there is
another reason for choosing an algorithm that does not require input excitation data -
input data in structural dynamics is frequently unreliable, contaminated by noise and
variability in all but the most controlled laboratory environments. Since, unavoidably.
21
output responses will themselves be affected by noise, the elimination of another source
of error (noise in the input) is very desirable.
22
ILS-UI Algorithm
Time Domain
Frequency Domain
System Identification
Input Known Output Known
Input Unknown Output Known
Input Known Output Known
Input Unknown Output Known
Input Unknown Limited Output Measurements
Figure 1.2, Classification of system identification and proposed study
23
Five techniques that meet the "no input information required" requirement have been
identified in the literature. They are (1) the Kalman Filtered Weighed Input (KF-WGI)
with running load approach (Hoshiya and Maruyama, 1987), (2) the Stochastic-Adaptive
techniques (Safak, 1989), (3) the Free-Decay Curve Analysis (Ibrahim, 1977; Kung et.
al.; 1989; Bedewi, 1986; Mickleborough and Pi, 1989; Hac and Spanos, 1990), (4) the
Stochastic Approach (Kozin, 1983; Wedig, 1983; Lee and Chen, 1988), and (5) the
Random Decrement Technique (Cole, 1973; Cadwell, 1987; Kung et. al., 1989; Yang et.
al., 1981, 1985; Tsai et. al., 1985, 1988). Derivatives of these techniques have been
developed, but they will not be discussed here. A summary of the properties of these
techniques is shown in Table 1.1.
Examination of Table 1.1 reveals that all five of the techniques found in the
literature have drawbacks. Four of them require modal information, which we have
already seen may cause problems, and the one that doesn't (Stochastic) is not applicable
at the element level and has limitations on the inputs and outputs. A sixth approach is
needed, and it is found in the ILS-UI algorithm.
The ILS-UI algorithm was first developed as a general concept in 1994 at the
University of Arizona by Wang. In the years that followed, Wang applied the algorithm
to specific applications and showed that it can identify stiffness and damping
characteristics for shear, truss, and beam structures (Wang, 1994, 1995, 1997). Wang
later showed that the ILS-UI algorithm can identify system characteristics from noise-
polluted responses. Further research showed that a Kalman filter can be used to predict
nodal responses and reduce the number of degrees of freedom needed to perform system
24
identification. In 2000, Ling showed that, using Taylor series expansion to remove
nonlinear characteristics, Rayleigh damping can be modeled and incorporated into the
algorithm. (Ling, 2000) (Wang had used viscous damping in work done to that point.)
In summary, there is a history of almost ten years of research showing that the ILS-
UI algorithm is a robust algorithm that can be applied to the nondestructive evaluation of
structures.
25
Table 1.1, Comparison of the proposed method with other SI techniques with unknown input
Limitation Limitation Need Identification Element Methods on Input on Output Modal
Properties [K] [C] {f} Level
KF-WGI with Yes No Yes No No Yes No running load Stochastic No No Yes No No No No Adaptive
6.5.3. Evaluation of the Simply Supported Test Results
The quantifiable changes in element stiffness values from the baseline configuration
to the damaged configuration are shown Table 6.9, under the column Changes in
Elemental Stiffness. Stiffness values change by large quantities from the baseline
configuration. Nevertheless, the damaged section of the beam still can be identified by
comparing the Changes in Elemental Stiffness to one another.
To begin, we look at Case 1. In this case the responses at Nodes 1, 2, 3, and 7 are
used to find the element stiffnesses. The predicted reduction in elemental stiffness from
the baseline (undamaged) to the damaged configuration are 63% and 69% for elements ®
and ®, but a 24% reduction for the beam section comprised of elements (D, @, ®, and
®. From the percentage reduction, it is clear that the damage is present in elements ®
and ®, because these two elements have larger stiffness reductions (63% and 69%) when
compared to the 24% reduction identified for elements (D, 0, ®, and ®. The number of
nodal responses used in the SI algorithm has been reduced from the optimum of seven
nodes to only four nodes, so the ILS-UI predicted element stiffnesses can no longer be
compared against the theoretical stiffnesses to identify damage. The only option left is to
compare the percentage reductions in element stiffness.
Similarly, nodal responses at Nodes 1, 3, 4, and 7 are used in Case 2. An 87%
reduction in stiffness values from the baseline to the damaged configuration is identified
for the beam section containing elements ® and ® (between Nodes 1 and 3); a 70%
reduction is noted for elements ®; and a 77% reduction occurs for the beam section
168
containing elements ®, ®, and ®. Again, the section containing elements ® and ® is
identified as the damaged section.
Case 3 uses the responses at Nodes 1, 3, 5 and 7 as input. The beam is divided in
three sections of equal length (25.4 cm). Similar to Cases 1 and 2, the damage is present
in the beam section bound by Nodes 1 and 3, i.e., 84% stiffness reduction there compared
to 66% for the other sections.
Lastly, Case 4 uses nodal responses at Nodes 1, 3, 6 and 7 as input. In this case
there is a 74% reduction in stiffness in the section between nodes ® and (D but only a
45% reduction in the other two sections.
The actual damage is present only in element ®, but all the test results indicate that
damage is present in both elements ® and ®. This is because of the limited number of
nodal responses used in the ILS-Ul algorithm. This causes the accuracy of the prediction
to degrade. With four responses, the damage can be identified to within one-third of the
beam's length; to go beyond that, more nodal responses must be used.
Despite the large measurement error in the sensors (accelerometer and
autocollimator) that restricts the use of large number of nodal responses in the beam, the
ILS-Ul algorithm is robust enough to identify damage in the beam even with a minimum
of information. It is believed that in the near future, when more accurate and affordable
sensors become available, the limitation in sensor's accuracy will no longer be a
restriction and the implementation of the ILS-Ul algorithm will be expanded to a new
level.
169
This dissertation proves that the ILS-UI algorithm works and can be used as a
method for detecting damage in structures. The algorithm works in both fixed-fixed and
simply supported beams despite large error in the sensor's measurements; this is an
indication of its wide applicability.
6.6. Summary
Several topics were discussed in this chapter. First, an intensive investigation to
determine the root cause of the ILS-UI algorithm's failure to converge was performed.
Amplitude and phase errors in the accelerometer's measurements were found to be the
root cause. Following this discovery, an alternative approach was developed to mitigate
the amplitude and phase shift errors.
The implementation of the alternative approach, using actual accelerometers and an
autocollimator to measure nodal responses for the fixed-fixed and simply supported
beams was given in detail. Nodal responses were measured for the beam with and
without damage. It was demonstrated that the ILS-UI algorithm successfully quantified
reduction in the beam's element stiffnesses and the location of damage was identified.
170
7. CHAPTER 7 - SUMMARY
7.1. Summary
The ILS-UI algorithm is a novel, nondestructive system identification technique.
Although it has the potential to be a powerful tool in the identification of structural
damage, to date it has not been validated with experimental data. The purpose of this
research was to validate the algorithm using measurements from fixed-fixed and simply
supported beams.
The development of the theoretical multi-degree-of-freedom beam models used in
the ILS-UI algorithm was given in detail. These models successfully identified defects
for both fixed-fixed and simply supported beams, using computer generated input.
As a prelude to the experimental validation, a simulation was performed to study
errors in the numerical integration of a digitized signal for three different rules:
trapezoidal, Simpson's and Boole's. It was shown that Simpson's rule and Boole's rule
yield smaller errors than the trapezoidal rule, especially when lower sampling rates are
used. Several post processing techniques to remove noise, to filter out high frequencies
and remove slope and offset from a data set were also demonstrated.
In the first phase of the validation experiments, the optimum number of node points
was determined for the fixed beam. Also, a method was developed to scale angular
response based on the measured transverse response. The ILS-UI algorithm was then
used to predict element stiffnesses for the fixed beam. The stiffnesses predictions did not
converge. This prompted an investigation to determine the root cause of the failure.
171
It was found that amplitude and phase errors in the accelerometer's measurements
were the root cause of the failure. After this was determined, an alternative approach was
developed to mitigate the amplitude and phase shift errors.
To validate the alternative approach, nodal responses were measured for the beam
with and without damage. The ILS-UI algorithm was demonstrated to successfully
quantify reduction in the beam's element stiffnesses and the location of damage was
identified.
7.2. Conclusions
The ILS-UI algorithm has been conclusively validated for fixed-fixed and simply
supported beams. That is to say, it can be used successfully to quantify reduction in the
beam's elemental stiffnesses and to identify the location of the damage.
The ILS-UI algorithm was also found to be very sensitive to the accelerometer scale
factor and cross coupling errors. Phase shift error among the measured nodal response
time histories was found to be a root cause of the ILS-UI algorithm failure to converge.
These errors were overlooked at the beginning of this research. It is the author's believe
that in the very near future, when the accelerometers are more accurate and more
affordable, the ILS-UI algorithm will find its place in many SI applications for both new
and existing structures.
172
7.3. Future Work
This dissertation only implements the ILS-UI algorithm in an individual beam with a
single damaged element. The following are recommended areas for future research:
1. Sensitivity of the ILS-UI algorithm to defect size
2. Application of the ILS-UI algorithm to more complicated, multiple beam
structures
3. Mitigation of the algorithm's sensitivity to amplitude and phase error, with the
goal of pinpointing the location of damage to a smaller section of the beam.
173
REFERENCES
Agbabian, M.S., Masri, S.F., Miller, R.K., and Caughey, T.K., System Identification Approach to Detection of Structural Changes, Journal of Engineering Mechanics, ASCE, Vol. 117, No. 2, pp. 370-390, 1991.
Aktan, A.E., Toksoy, T., and Hosahalli, S., Implication of Modal Test and Structural Identification on Active Structural Control, Proceedings of the U.S. Nat. Eorkshop on Structural Control Res., University of Southern California, Los Angeles, CA, 1990.
Aktan, A.E., Zwick, M., Miller, R.A., and Shahrooz, B.M., Nondestructive and Destructive Testing of a Decommissioned RC Highway Slab Bridge and Associated Studies, Transportation Research Record, 1371, 142-153, 1988.
Aktan, E., Catbas, N., Turer, A., and Zhang, Z., Structural Identification: Analytical Aspects, Journal of Engineering Mechanics, ASCE, pp. 817-829,1998.
Aktan, E., Farhey, D.N., Helmicki, A.J., Brown, D.L., Hunt, V.J., Lee, K.-L., Levi, A., Structural Identification for Condition Assessment: Experimental Arts, Journal of Structural Engineering, pp. 1674-1684, 1997.
Bedewi, N.E., The Mathematical Foundation of the Auto and Cross Random Decrement Techniques and the Development of a System Identification Technique for the Detection of Structural Deterioration, Ph.D. Thesis, The University of Maryland, 1986.
Bickford, W. B., A First Course in the Finite Element Method, Second Edition, Irwin, 1994.
Brockwell, P.J., and Davis, R.A., Introduction to Time Series and Forecasting, Springer-Verlag,N.Y, 1996.
Caldwell, D.W., The Measurement of Damping and the Detection of Damage in Linear and Nonlinear Systems by the Random Decrement Technique, Ph.D. Thesis, The University of Maryland, 1987.
Cole, H.J., On-line Failure Detection and Damping Measurement of Aerospace Structure by Random Decrement Signatures, NASA Contractor Report, NASA CR-2205, Washington D.C., March 1973.
Clough, R. and Penzien, L, Dynamics of Structures, John Wiley, 1998.
Hac, A. and Spanos, P.D., Time Domain Method for Parameter System Identification, J. of Vibration and Acoustics, 112, pp.281-287,1990.
Hoshiya, M., and Maruyama, O., Identification of Running Load and Beam System, Joumal of Engineering Mechanics, ASCE, 113(4), pp. 813-824, 1987.
Hoshiya, M., and Saito, E., Structural Identification by Extended Kalman Filter, Joumal of Engineering Mechanics, ASCE, Vol. 110, No. 12, pp. 1757-1770, 1994.
Hoshiya, M., and Sutoh, A., Kalman Filter-Finite Element Method in Identification, Joumal of Engineering Mechanics, ASCE, Vol. 199, No. 2, pp. 197-210, 1993.
Ibanez, P., Identification of Dynamic Parameters of Linear & Nonlinear Structural Models from Experiment Data, Nuclear Eng. Design, pp.25-30, 1972.
Ibrahim, S.R. and Mikulcik, E.C., A method for the Direct Identification of Vibration Parameters from the Free Response, The Shock and Vibration Bulletin, 47, Part 4, pp.183-196, 1977.
Ibrahim, S.R., Random Decrement Technique for Modal Identification of Structures, Joumal of Spacecraft and Rockets, 14(11), 696-700, 1977.
Ibrahim, S.R., Time-Domain Quasi-linear Identification of Nonlinear Dynamic System, AIAA Paper 83-0811, 1983.
Imai, H., Yun, C.B., Maruyama, O. and Shinozuka, M., Fundamentals of System Identification in Stmctural Dynamics, Technical Report, NCEER-89-008, Jan 26, 1989.
Kalman, R.E., A New Approach to Linear Filtering and Prediction Problems, Journal of Basic Engineering, Vol. 82, No. 1, pp. 35-45, 1960.
Koh, C.G. and See, L.M., Identification and Uncertainty Estimation of Structural Parameters, Journal of Engineering Mechanics, ASCE, Vol. 120, No. 6, pp. 1219-1236, 1994.
Koh, C.G., See, L.M. and Balendra, T., Estimation of Structural Parameters in Time Domain: A substructure Approach, Journal of Earthquake Engineering and Structural Dynamics, Vol. 10, pp.787-801, 1991.
Kozin, F., Estimation of Parameters for Systems Driven by White Noise Excitation, Proc. of lUTAM Symposium, Frankfurt/Oder (GDR), Hennig Klaus Ed., pp. 163-173, 1983.
175
Kung, D.N., Yang, J.C.S., Bedewi, N.E. and Tsai, W.H., Time Domain System Identification Techniques Based on Impulsive Loading for Damage Detection, Proc. Of 8*'^ Int. Symp. On Offshore Mech. And Artie Engineering, pp.307-317, 1989.
Lee, A.C. and Chen, J.H., Modal Parameter Estimation for Randomly Excited Structural Systems with Unmeasured Input, Proc. of Int'l Workshop on Nondestructive Evaluation for Performance of Existing Structures, Agbabian, M.S. and Masri, S.F., Eds., USC, Los Angeles, CA, 1988.
Ling, X., Haldar, A., and Vo, P., "Experimental Verification of A Novel Time-Domain System Identification Technique," Specialty Conference on Probabilistic Mechanics and Structural Reliability, University of Notre Dame, Paper PMC2000-086 (CD-ROM), 2000.
Ling, X., "Linear and Nonlinear Time Domain System Identification at Element Level for Structural Systems with Unknown Excitation", Ph.D. Thesis, The University of Arizona, 2000.
Mickleborough, N.C. and Pi, Y.C., System Modal Identification Using Free Vibration Data, Proc. Of Japan Society of Civil Engineers, 410, pp.217-228, 1989.
Oppenheim, A.V., and Schafer, R.W., Digital Signal Processing, Prentice Hall, Englewood Cliffs, N.J, 1975.
Pozrikidis, C., Numerical Computation in Science and Engineering, Oxford University Press, 1998.
Safak, E. Adaptive Modeling, Identification and Control of Dynamic Structural System I; Theory, Journal of Engineering Mechanics, ASCE, pp.2386-2405, 1989.
Shinozuka, M., Yun, C.-B., and Imai, H., Identification of Linear Structural Dynamic Systems, Journal of Engineering Mechanics, ASCE, Vol. 108, No. 1, pp. 1371-1390, 1982.
Thomson, W.T., Theory of Vibration with Applications, 4^"' edition. Prentice Hall, 1993.
Tsai, W.H., Kung, D.N. and Yang, J.C.S., Application of System Identification Technique to Damage Detection and Location in Offshore Platform, Proc. of 1^^ Int. Symp. On Offshore Mech. And Artie Engineering, 1988.
Tsai, W.H., Yang, J.C.S. and Chen, R.Z., Detection of Damages in Structures by Cross Random Decrement Methods, Proc. of 3'^'' Int. Modal Analysis Conference, 1985.
176
Vo, P., Haldar, A., "Post-processing of linear accelerometer data in structural identification". Journal of Structural Engineering, Vol.30, No.2, pp. 123-130, July-September 2003.
Vo, P., Haldar, A., "Health Assessment of Beams - Theoretical and Experimental Investigations", Journal of Structural Engineering. Currently under review.
Vo, P., Haldar, A., "Damage Identification of the Fixed-Fixed and Simply Supported Beams", Journal of Engineering Mechanics. Currently under review.
Wang, D., and Haldar, A., "System Identification with Limited Observations and Without Input," Journal of Engineering Mechanics, ASCE, 123(5), 504-511, 1997.
Wang, D., and Haldar, A., Element-Level System Identification With Unknown Input, Journal of Engineering Mechanics, ASCE, Vol. 120, No. 1, pp. 159-176, 1994.
Wang, D., and Haldar, A., System Identification With Limited Observations and Without Input, Journal of Engineering Mechanics, ASCE, Vol. 123, No. 5, pp. 504-511, 1997.
Wang, D., Element Level Time Domain System Identification Techniques With Unknown Input Information, Ph.D. Thesis, The University of Arizona, 1995.
Wedig, W., Fast Algorithms in Parameter Identification of Dynamic Systems, Proc. lUTAM Symposium on Random Vibration and Reliability, Hennig, K., Ed. Akadamie-Verlag, Berlin, pp.217-227, 1983.
Yang, J.C.S., Aggour, M.S., Dagalakis, N. and Miller, F., Damping of an Offshore Platform Model by Random Decrement Method, Proc. of 2"*^ Specialty Conference, ASCE, pp.819-832, 1981.
Yang, J.C.S., Tsai, T., Tsai, W.H. and Chen R.Z., Detection and Identification of Structural Damage from Dynamic Response Measurements, Proc. of 4*"^ Int. Symp. on Offshore Mech. And Artie Engineering, pp.496-504, 1985.
Yun, C.B. and Shinozuka, M., Identification of Nonlinear Structural Dynamic Systems, J. of Struc. Mech., Vol. 8, pp. 187-203, 1980.
Yun, C.B., Lee, H.J. and Lee, G.G., Sequential Prediction-Error Method for Structural Identification, Journal of Engineering Mechanics, Vol. 123, No. 2, pp. 115-122, 1997.